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    题名: 系列平行圖的長方形數與和絃圖數
    The Boxicity and Chordality of a Series-Parallel Graph
    作者: 周佳靜
    贡献者: 張宜武
    周佳靜
    关键词: 和弦圖數
    和弦圖
    平面圖
    系列平行圖
    Chordality
    Chordal Graphs
    Planar Graphs
    Series-Parallel Graphs
    Boxicity
    日期: 2011
    上传时间: 2016-05-10 19:01:54 (UTC+8)
    摘要: 一個圖形G = (V,E)，如果可以找到最小k個和弦圖，則此圖形G = (V,E)的和弦圖數是k。
    在這篇論文中，我們呈現存在一個系列平行圖的boxicity是3，且和弦圖數是1或2，存在一個平面圖形的和弦圖數是3。
    The chordality of G = (V,E) is dened as the minimum k such that we can write E = E1n...nEk, where each (V,Ei) is a chordal graph.
    In this thesis, we present that (1) there are series-parallel graphs with boxicity 3, (2) there are series-parallel graphs with chordality 1 or 2, and (3) there are planar graphs with chordality 3.
    Abstract iii
    中文摘要iv
    1 The Chordality of a Graph 1
    1.1 History of Chordal Graph and Boxicity . . . . . . . 1
    1.2 The De nition and Theorems of Chordality . . . . . . 2
    1.3 Examples of Chordality . . . . . . . . . . . . . . ..7
    2 A Necessary Condition 11
    2.1 The Chordality of BPn . . . . . . . . . . . . . . . .11
    2.2 The Counter Example . . . . . . . . . . . . . . . . 13
    3 Series-Parallel Graphs 14
    3.1 The De nition of Treewidth . . . . . . . . . . . . . 14
    3.2 The De nition of Series-Parallel Graphs . . . . . . . 17
    3.3 The Treewidth and Chordality of Series-Parallel Graphs . . . 22
    4 The Boxicity of a Graph 24
    4.1 The De nition of Boxicity . . . . . . . . . . . . . ..24
    4.2 The Boxicity of Series-Parallel Graphs . . . . . . . 27
    References 32
    參考文獻: [1] P. Buneman, A characterization of rigid circuit graphs, Discrete Mathematics, 9 (1974), pp. 205-212.
    [2] M. Cozzens and F. Roberts, On dimensional properties of graphs, Graphs and Combinatorics, 5 (1989), pp. 29-46.
    [3] G. Dirac, A property of 4-chromatic graphs and some remarks on critical graphs, J. London Math. Soc., 27 (1952), pp. 85-92.
    [4] R. Duffin, Topology of series-parallel nextworks, J. Math. Anal. Appl., 10(1965), pp. 303-318.
    [5] F. Gavril, The intersection graphs of subtrees in trees are exactly the chordal graphs, Journal of Combinatorial Theory (B), 16 (1974), pp. 47-56.
    [6] M. Golumbic, Algorithmic graph theory and perfect graphs, Academic Press,(1980).
    [7] T. A. McKee and E. R. Scheinerman, On the chordality of a graph, Graph Theory, 17 (1993), pp. 221-232.
    [8] E. Scheinerman, Intersection classes and multiple intersection parameters of graphs, Ph.D. thesis, Princeton University, (1984).
    [9] C. Thomassen, Interval representations of planar graphs, Journal of Combinatorial Theory (B), 40 (1986), pp. 9-20.
    [10] J. Walter, Representations of chordal graphs as subtrees of a tree, J. Graph Theory, 2 (1978), pp. 265-267.
    描述: 碩士
    國立政治大學
    應用數學系數學教學碩士在職專班
    98972010
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0098972010
    数据类型: thesis
    显示于类别:[應用數學系] 學位論文

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